Geometric rate of growth in population-size-dependent branching processes
- 1 March 1984
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (1) , 40-49
- https://doi.org/10.2307/3213662
Abstract
We consider a branching-process model {Zn}, where the law of offspring distribution depends on the population size. We consider the case when the meansmn(mnis the mean of offspring distribution when the population size is equal ton) tend to a limitm >1 asn→∞. For a certain class of processes {Zn} necessary conditions for convergence inL1andL2and sufficient conditions for almost sure convergence and convergence inL2ofWn= Zn/mnare given.Keywords
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